1. Field of the Invention
The present invention relates to a Multiple Input Multiple Output (MIMO) system and, in particular, to a method and apparatus for transmitting and receiving signals using a codebook which maps each codeword to at least two different antennas in a MIMO system.
2. Description of the Related Art
Recently, extensive research has focused on Orthogonal Frequency Division Multiple Access (OFDMA) and Single Carrier-Frequency Division Multiple Access (SC-FDMA) to implement high speed data transmission on wireless channels in wireless communication system. In Long Term Evolution (LTE), as a next generation wireless communication standard, Orthogonal Frequency Division Multiplexing (OFDM) is adopted for downlink transmission, and the SC-FDMA is used for uplink transmission. In the OFDM system, due to its high Peak-to-Average Power Ratio (PAPR) it is required to increase the back-off of the input signal of the power amplifier in order to prevent non-linear distortion of the signal, thus limits the maximum transmission power, resulting in degradation of the power efficiency. The back-off is needed to limit the transmit power to the maximum value of a power amplifier so as to guarantee the linearity of the transmit signal. For example, assuming that a power amplifier has a maximum value of 23 dBm and the back-off is 3 dB, the maximum value of transmission power becomes 20 dBm. This does not cause a problem in OFDMA as the downlink multiplexing technique since the transmitter exists in the base station which is not limited in power. In a case where OFDMA is adopted as the uplink multiplexing, however, the transmitter of the power-constrained user equipment is limited in transmission power, resulting in a reduction of the base station coverage. As a result, SC-FDMA has been adopted by the 3rd Generation Partnership Project (3GPP) for use in the LTE uplink as an alternative to OFDM.
Various wireless communication technologies have been developed for supporting diverse multimedia services in the recent wireless communication environment, in which a high data rate is required for providing high quality multimedia services. In order to meet the high data rate requirements, extensive research is being conducted, and MIMO is one of the underlying technologies for that purpose.
MIMO is the technology for expanding the channel capacity within the limited frequency resource by using multiple antennas. Using multiple antennas in a scattering environment, it is possible to secure the channel capacity logically in proportion to the number of the antennas. In order to improve the data transmission efficiency in a MIMO system, the MIMO system is required to encode data in advance. This process is referred to as precoding. The rule for precoding data is represented by a set of precoding matrices which is referred to as a codebook. In LTE-Advanced (LTE-A), the MIMO technology using precoding matrices is one of the proposed key technologies for performance improvement of uplink transmission in single-user and multi-user environments. The codebook-based precoding is being considered as a technology for simply improving the LTE system. Although the aforementioned SC-FDMA is adopted as a promising uplink technology thanks to its low PAPR over OFDM, SC-FDMA causes the following problems when combined with the precoding-based MIMO technology. If multiple antenna precoding matrices are applied to the SC-FDMA and if a precoding matrix mixing the data of different layers is selected, the PAPR increases at each antenna.
In the case of the SC-FDMA MIMO system using 4 transmit antennas and 4 receive antennas, a maximum of 4 ranks of data channels can be generated between the transmit and receive antennas, using different precoding matrices. For example, if it is determined that a rank-1 channel is established between the transmit and receive antennas, the preceding matrices as shown in Table 1 can be used.
Table 1 sets forth an exemplary rank-1 codebook of the precoding matrices for 4 transmit antennas.
TABLE 1         [                            1                                      0                                      0                                      0                      ]           [                            0                                      1                                      0                                      0                      ]           [                            0                                      0                                      1                                      0                      ]           [                            0                                      0                                      0                                      1                      ]        1    2    ⁡      [                            1                                      1                                      1                                                  -            j                                ]        1    2    ⁡      [                            1                                      1                                      j                                                  -            1                                ]         1    2    ⁡      [                            1                                      1                                                  -            1                                                j                      ]        1    2    ⁡      [                            1                                      1                                                  -            j                                                1                      ]        1    2    ⁡      [                            1                                      1                                                  -            j                                                            -            j                                ]        1    2    ⁡      [                            1                                      j                                      1                                                  -            1                                ]              1      2        ⁡          [                                    1                                                j                                                j                                                j                              ]        ⁢              1    2    ⁡      [                            1                                      j                                                  -            1                                                1                      ]         1    2    ⁡      [                            1                                      j                                                  -            1                                                            -            j                                ]        1    2    ⁡      [                            1                                      j                                                  -            j                                                            -            1                                ]        1    2    ⁡      [                            1                                                  -            1                                                1                                      j                      ]        1    2    ⁡      [                            1                                                  -            1                                                j                                      1                      ]              1      2        ⁡          [                                    1                                                              -              1                                                            j                                                              -              j                                          ]        ⁢              1    2    ⁡      [                            1                                                  -            1                                                            -            1                                                            -            1                                ]         1    2    ⁡      [                            1                                                  -            1                                                            -            j                                                j                      ]        1    2    ⁡      [                            1                                                  -            j                                                1                                      1                      ]        1    2    ⁡      [                            1                                                  -            j                                                1                                                  -            j                                ]        1    2    ⁡      [                            1                                                  -            j                                                j                                                  -            1                                ]        1    2    ⁡      [                            1                                                  -            j                                                            -            1                                                j                      ]        1    2    ⁡      [                            1                                                  -            j                                                            -            j                                                1                      ]  
In Table 1, each preceding matrix has 4 rows (i.e. four antennas) and 1 column (i.e. rank-1, i.e. one layer). In the rank-1 preceding matrix, the number of layers is 1 and thus the outputs of the individual antennas are not mixed. In this case, there is no increase in PAPR at the power amplifier of each antenna.
If it is determined that a rank-2 channel is established between the transmit and receive antennas, the precoding matrices as shown in Table 2 can be used.
Table 2 sets forth an exemplary rank-2 codebook of the precoding matrices for 4 transmit antennas.
TABLE 2      1    2    ⁡      [                            1                          0                                      0                          1                                                  -            j                                    0                                      0                          1                      ]        1    2    ⁡      [                            1                          0                                      0                          1                                      0                          j                                      1                          0                      ]        1    2    ⁡      [                            1                          0                                      1                          0                                      0                          1                                      0                                      -            1                                ]        1    2    ⁡      [                            1                          0                                      0                          1                                                  -            1                                    0                                      0                                      -            j                                ]         1    2    ⁡      [                            1                          0                                      0                          1                                      1                          0                                      0                          j                      ]        1    2    ⁡      [                            1                          0                                      1                          0                                      0                          1                                      0                          1                      ]        1    2    ⁡      [                            0                          1                                      0                                      -            1                                                1                          0                                      1                          0                      ]        1    2    ⁡      [                            1                          0                                      0                          1                                      0                          j                                                  -            1                                    0                      ]         1    2    ⁡      [                            0                          1                                      0                                      -            1                                                1                          0                                                  -            1                                    0                      ]        1    2    ⁡      [                            1                          0                                      0                          1                                      j                          0                                      0                          1                      ]        1    2    ⁡      [                            1                          0                                      j                          0                                      0                          1                                      0                          j                      ]        1    2    ⁡      [                            1                          0                                                  -            j                                    0                                      0                          1                                      0                          j                      ]         1    2    ⁡      [                            0                          1                                      1                          0                                                  -            j                                    0                                      0                          j                      ]        1    2    ⁡      [                            1                          0                                      0                          1                                      j                          0                                      0                                      -            1                                ]        1    2    ⁡      [                            1                          0                                      0                          1                                                  -            1                                    0                                      0                          j                      ]        1    2    ⁡      [                            1                          0                                      j                          0                                      0                          1                                      0                                      -            j                                ]         1    2    ⁡      [                            1                          0                                      0                          1                                      0                                      -            j                                                            -            j                                    0                      ]        1    2    ⁡      [                            1                          0                                      0                          1                                                  -            j                                    0                                      0                                      -            1                                ]        1    2    ⁡      [                            0                          1                                      0                                      -            j                                                1                          0                                                  -            j                                    0                      ]        1    2    ⁡      [                            0                          1                                      1                          0                                      0                          1                                                  -            j                                    0                      ]  
In Table 2, each precoding matrix has 4 rows (i.e. four antennas) and 2 columns (i.e. rank-2, i.e. two layers). Since one zero element is included in each row even with two layers, the layers are not mixed. That is, there is no increase in PAPR at the power amplifier of each antenna.
If it is determined that a rank-3 channel is established between the transmit and receive antennas, the precoding matrices as shown in Table 3 can be used.
Table 3 sets forth an exemplary rank-3 codebook of the precoding matrices for 4 transmit antennas.
TABLE 3      1          2      ⁢              2              ⁡      [                            1                                      -            j                                    0                                                  -            j                                                -            j                                    0                                                  -            j                                    0                          1                                                  -            j                                    0                                      -            j                                ]        1          2      ⁢              2              ⁡      [                            1                                      -            j                                    0                                                  -            j                                                -            j                                    0                                      j                          0                          1                                      j                          0                                      -            j                                ]        1          2      ⁢              2              ⁡      [                            1                                      -            j                                    0                                      j                                      -            j                                    0                                                  -            j                                    0                          1                                      j                          0                                      -            j                                ]         1          2      ⁢              2              ⁡      [                            1                                      -            j                                    0                                      j                                      -            j                                    0                                      j                          0                          1                                                  -            j                                    0                                      -            j                                ]        1          2      ⁢              2              ⁡      [                            1                                      -            j                                    0                                                  -            j                                                -            j                                    0                                                  -            j                                    0                          1                                      j                          0                          j                      ]        1          2      ⁢              2              ⁡      [                            1                                      -            j                                    0                                                  -            j                                                -            j                                    0                                      j                          0                          1                                                  -            j                                    0                          j                      ]         1          2      ⁢              2              ⁡      [                            1                                      -            j                                    0                                      j                                      -            j                                    0                                                  -            j                                    0                          1                                                  -            j                                    0                          j                      ]        1          2      ⁢              2              ⁡      [                            1                                      -            j                                    0                                      j                                      -            j                                    0                                      j                          0                          1                                      j                          0                          j                      ]        1          2      ⁢              2              ⁡      [                            1                                      -            j                                    0                                                  -            j                                    j                          0                                      1                          0                          1                                                  -            1                                    0                                      -            j                                ]         1          2      ⁢              2              ⁡      [                            1                                      -            j                                    0                                                  -            j                                    j                          0                                                  -            1                                    0                          1                                      1                          0                                      -            j                                ]        1          2      ⁢              2              ⁡      [                            1                                      -            j                                    0                                      j                          j                          0                                      1                          0                          1                                      1                          0                                      -            j                                ]        1          2      ⁢              2              ⁡      [                            1                                      -            j                                    0                                      j                          j                          0                                                  -            1                                    0                          1                                                  -            1                                    0                                      -            j                                ]         1          2      ⁢              2              ⁡      [                            1                                      -            j                                    0                                                  -            j                                    j                          0                                      1                          0                          1                                      1                          0                          j                      ]        1          2      ⁢              2              ⁡      [                            1                                      -            j                                    0                                                  -            j                                    j                          0                                                  -            1                                    0                          1                                                  -            1                                    0                          j                      ]        1          2      ⁢              2              ⁡      [                            1                                      -            j                                    0                                      j                          j                          0                                      1                          0                          1                                                  -            1                                    0                          j                      ]         1          2      ⁢              2              ⁡      [                            1                                      -            j                                    0                                      j                          j                          0                                                  -            1                                    0                          1                                      1                          0                          j                      ]  
In Table 3, each precoding matrix has 4 rows (i.e. four antennas) and 3 columns (i.e. rank-3, i.e. three layers). Assuming that a precoding matrix (1) is selected from Table 3:
                              1                      2            ⁢                          2                                      ⁡                  [                                                    1                                                              -                  j                                                            0                                                                                      -                  j                                                                              -                  j                                                            0                                                                                      -                  j                                                            0                                            1                                                                                      -                  j                                                            0                                                              -                  j                                                              ]                                    (        1        )            the outputs of four antennas are y1, y2, y3, and y4; the symbol data mapped to layer 1 (layer#1) is x1, the symbol data to layer 2 (layer#2) is x2, and the symbol data to layer 3 (layer#3) is x3. The relation between the layers and antennas can be expressed by Equation (2):
                              [                                                                      y                  ⁢                                                                          ⁢                  1                                                                                                      y                  ⁢                                                                          ⁢                  2                                                                                                      y                  ⁢                                                                          ⁢                  3                                                                                                      y                  ⁢                                                                          ⁢                  4                                                              ]                =                                            1                              2                ⁢                                  2                                                      ⁡                          [                                                                    1                                                                              -                      j                                                                            0                                                                                                              -                      j                                                                                                  -                      j                                                                            0                                                                                                              -                      j                                                                            0                                                        1                                                                                                              -                      j                                                                            0                                                                              -                      j                                                                                  ]                                ⁡                      [                                                                                x                    ⁢                                                                                  ⁢                    1                                                                                                                    x                    ⁢                                                                                  ⁢                    2                                                                                                                    x                    ⁢                                                                                  ⁢                    3                                                                        ]                                              (        2        )            
In Equation (2), the output of antenna 1 (antenna#1) is expressed by
      y    ⁢                  ⁢    1    =            1              2        ⁢                  2                      ⁢                  (                              x            ⁢                                                  ⁢            1                    -                      jx            ⁢                                                  ⁢            2                          )            .      That is, the symbol data x1 mapped to layer 1 (layer#1) and the symbol data x2 mapped to layer 2 (layer#2), by the elements 1 and −j of the first row of the precoding matrix are mixed to be output and thus increases the PAPR of the power amplifier of antenna 1 (antenna#1). The output of antenna 2 (antenna#2) is expressed by
      y    ⁢                  ⁢    2    =            1              2        ⁢                  2                      ⁢                  (                                            -              j                        ⁢                                                  ⁢            x            ⁢                                                  ⁢            1                    -                      j            ⁢                                                  ⁢            x            ⁢                                                  ⁢            2                          )            .      That is, the symbol data x1 mapped to layer 1 (layer#1) and the symbol data x2 mapped to layer 2 (layer#2) by the elements −j and −j of the second row of the precoding matrix are mixed to be output and thus increases the PAPR of the power amplifier of antenna 2 (antenna#2). The output of antenna 3 (antenna#4) is expressed by
      y    ⁢                  ⁢    3    =            1              2        ⁢                  2                      ⁢                  (                                            -              j                        ⁢                                                  ⁢            x            ⁢                                                  ⁢            1                    +                      x            ⁢                                                  ⁢            3                          )            .      That is, the symbol data x1 mapped to layer 1 (layer#1) and the symbol data x2 mapped to layer 2 (layer#2) by the elements −j and 1 of the third row of the precoding matrix are mixed to be output and thus increases the PAPR of the power amplifier of antenna 3 (antenna#3). The output of antenna 4 (antenna#4) is expressed by
      y    ⁢                  ⁢    4    =            1              2        ⁢                  2                      ⁢                  (                                            -              j                        ⁢                                                  ⁢            x            ⁢                                                  ⁢            1                    -                      j            ⁢                                                  ⁢            x            ⁢                                                  ⁢            3                          )            .      That is, the symbol data x1 mapped to layer 1 (layer#1) and the symbol data x2 mapped to layer 2 (layer#2) by the elements −j and −j of the fourth row of the precoding matrix are mixed to be output and thus increases the PAPR of the power amplifier of antenna 3 (antenna#4).